Biology Reference
In-Depth Information
2.5
2
1.5
1
α
α
α
0.5
0
−
0.5
−
1
−
1.5
−
2
−
2.5
0
2
4
6
8
10
12
14
A
Time
2
1.5
1
0.5
0
−
0.5
−
1
−
1.5
−
2
0
2
4
6
8
10
12
14
2
p
4
p
6
p
Time
B
β
β
β
FIGURE 11-10.
Graphs of
a
cos(t) with
a >
0 (panel A) and cos(
b
t) with
b >
1 (panel B).
b
b >
period). In Figure 11-10(B) we give the graph of cos(
t)with
1.
b
Note that the larger
is, the higher the frequency and the shorter
the period.
The parameter
g
affects the phase shift of the graph. The graph is shifted
to the left when
< 0. It can also be
interpreted as the time value at which the periodic or rhythmic pattern
begins. The graph of cos(t
g >
0 and shifted to the right when
g
þ p
/4) is shown in Figure 11-11(A), and the
graph of cos(2t
þ p
/4)
¼
cos(2(t
þ p
/8)) is shown in Figure 11-11(B).
A cosine-like pattern (or possibly a truncated cosine) is often found
in circadian rhythm data, but there are also some variations. The
amplitude might vary from one cycle to the next as in the graph shown
in Figure 11-12(A), or the period may change by compressing
(or expanding) as in the graphs shown in Figure 11-12(B).
